TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/seam-partner-original-action-20261015/PROOF.txt
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Inclusive original lines: 13-63
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000013 | 1. ORIGINAL DATA AND THE THREE DIFFERENT OBJECTS
000014 | 
000015 | P1 at tfpt_1_architecture_e8.tex:167-188 stipulates an oriented primitive
000016 | reflection-positive seam kernel, unit winding and c3=1/(8pi). P2 stipulates
000017 | five carrier slots with the 3+2 split. Its representation consequences include
000018 | E=C^5=E3 direct-sum E2 and S+=Lambda_even E, with the given hypercharges.
000019 | The original carrier source :573-668 explicitly identifies Lambda^0 E with
000020 | the internal nu^c label. It is NOT the physical vacuum of an affine field net.
000021 | 
000022 | Write epsilon_i for exterior multiplication by u_i and iota_i for contraction.
000023 | The quadratic Clifford representation of so(10) has the root operator
000024 | 
000025 |     A=E_(e1+e4)=epsilon_1 epsilon_4,
000026 |     A 1=u_1 wedge u_4.
000027 | 
000028 | This fixes an actual nonzero operator and its carrier action, with the stated
000029 | root-vector convention. It is part of the original quadratic-transport algebra
000030 | at architecture :1569-1584; no new interaction has been selected.
000031 | 
000032 | Keep these types separate:
000033 |   (a) A is a Lie-algebra operator in the adjoint 45;
000034 |   (b) A1 is a vector in the half-spinor 16, with weight w_empty+e1+e4;
000035 |   (c) |e1+e4>=J_(e1+e4),-1 Omega is an affine root-current state of weight 1.
000036 | The known lattice map M r0=e1+e4 relates root coordinates. It does not identify
000037 | (b) with (c), or the exterior unit 1 with the physical vacuum Omega.
000038 | An infinite affine module is not identified with a finite 16 by this calculation.
000039 | 
000040 | 2. WHICH CHARGE IS NEUTRAL?
000041 | 
000042 | On the carrier let N_i=epsilon_i iota_i. Original P2 hypercharge is
000043 | 
000044 |     Y=-(N1+N2+N3)/3+(N4+N5)/2.
000045 | 
000046 | The CAR identity gives [N_i,A]=(delta_i1+delta_i4) A. Therefore
000047 | 
000048 |     [Y,A]=A/6.
000049 | 
000050 | The six A_(ia)=epsilon_i epsilon_a, i=1,2,3 and a=4,5, transform as
000051 | (3,2)_(1/6). With T3=(N4-N5)/2, the a=4 and a=5 electric charge shifts are
000052 | 2/3 and -1/3. Changing the weak basis interchanges these labels; neither is zero.
000053 | These are charge changes of the root operator and charges of the carrier vector
000054 | A1 relative to the exterior unit. No physical gauge-boson/fermion equivalence is
000055 | inferred from their common representation label.
000056 | 
000057 | The previous fold has a different charge: Q'=2(H3+H6). Its carrier action has
000058 | Q_E=2 diag(0,0,1,0,0), and [dGamma(Q_E),A]=0. This correctly reproduces the
000059 | previous statement that r0 is source-charge neutral. On the six root directions
000060 | the Q' charges are (0,0,0,0,2,2). Thus Q' is not hypercharge and is not central
000061 | under the full color action. This distinction does not invalidate the original
000062 | zero-source-charge calculation; it prevents importing a stronger neutrality.
000063 | FOLD-AUDIT.md:168-230 explicitly conditions this dictionary on the E8 extension.